Turkey's President Tayyip Erdogan (2nd R) walks with his Russian counterpart Vladimir Putin prior to their meeting at the Group of 20 (G20) leaders summit in the Mediterranean resort city of Antalya, Turkey, November 16, 2015. Photo: Reuters/Kayhan Ozer/Pool

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The Kremlin said on Tuesday it would take more than a few days to mend Russia's relations with Ankara, after Turkish President Tayyip Erdogan expressed regret over the downing of a Russian military plane last year.

Russian President Vladimir Putin had said an apology from Erdogan was the condition for repairing relations between the two countries, which were poisoned when the Russian jet was shot down near the Syrian-Turkish border in November.

After writing to Putin to voice his regret over the incident, Erdogan said he now believed that Ankara would normalize relations with Moscow "rapidly".

The Kremlin was more cautious on Tuesday.

"One should not think it possible to normalize everything within a few days, but work in this direction will continue," Kremlin spokesman Dmitry Peskov told a conference call with journalists.

"President Putin has expressed more than once his willingness to uphold good relations with Turkey and the Turkish people," Peskov said. "Now a very important step has been made in this respect."

Putin and Erdogan will hold a telephone conversation at Moscow's initiative on Wednesday, Peskov said.

Ankara said it shot down the plane because it entered Turkish airspace, an allegation Moscow denies. The Russian pilot ejected from the plane but was killed by gunfire from rebels on the ground in Syria as he parachuted down to earth.

Moscow, which imposed economic sanctions on Ankara over the downed plane, had said that apart from official apologies it also wanted Turkey to pay compensation for the incident.

However, Turkish Prime Minister Binali Yildirim said on Tuesday that Turkey would not pay compensation to Russia over the downing of the plane.

Yildirim also told reporters in parliament that legal proceedings were underway against an individual allegedly responsible for the killing of the Russian pilot.